Along with raising the tension and fear throughout season 1, Lexi's death was vital to the plot. Throughout season 1, Stefan and Damon try to avoid any attention being drawn to them, especially when it comes from law enforcement.
However, around the time of Vicki's death, suspicions are high and Damon, as per usual, enacts a morally ambiguous plan to save himself and Stefan: frame his behavior on Lexi so that the police no longer suspect him. Though it's an unfortunate, Lexi's death does in fact help the Salvatores from being condemned.
Additionally, Lexi's death continues the rising tensions between Stefan and Damon. At this point in the show, the brothers are definitely in a sort of rivalry wherein Stefan is the good vampire and the hero and Damon is the morally grey and dangerous monster.
Lexi's death only emphasizes these points. Plus, Damon murdering Lexi is a betrayal of Stefan as well because of their close friendship. Therefore, Lexi's death keeps these themes moving until they finally explode at the end of the season.
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